Cock came from a large and relatively prosperous local family whose members played an important role in the government of the Port of Sandwich throughout the fifteenth and sixteenth centuries. He was already a member of the governing elite of Sandwich when he was elected to his only Parliament in 1429, having been chosen as mayor in 1424 and again three years later. It is unclear when he was first chosen as a jurat, although he was serving as such in December 1431 from when the records of the annual elections are extant. As one of the leading members of the jurats’ bench, he served as deputy mayor to John Smith I* on at least two occasions in 1432 and he was one of the three custodians of the keys to the common chest between 1432 and 1436.
Little is know of Henry’s private affairs. On 22 Mar. 1426 he and his wife received a papal indult from Martin V allowing them their own altar.
